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Answer:

[tex]\rf x=\frac{\sqrt{10}}{4},\:x=-\frac{\sqrt{10}}{4}[/tex]

step wise explanation:

  • [tex]\rf 8x^2 - 3=2[/tex]

change sides:

  • [tex]\rf 8x^2 =2+3[/tex]

simplify

  • [tex]\sf 8x^2 = 5[/tex]

change sides:

  • [tex]\sf x^2 = \frac{5}{8}[/tex]

changing square to square root:

  • [tex]x = \pm \sqrt{\frac{5}{8} }[/tex]

normal answer:

  • [tex]\rf \sqrt{\frac{5}{8} } \ \ or -\sqrt{\frac{5}{8} }[/tex]

apply radical rule of

  • [tex]\rf \frac{\sqrt{5} }{\sqrt{8} } } \ \ or \rf -\frac{\sqrt{5} }{\sqrt{8} } }[/tex]
  • [tex]\sf \frac{\sqrt{5}}{2\sqrt{2}} \ \ or \ \ \sf -\frac{\sqrt{5}}{2\sqrt{2}}[/tex]

rationalise:

  • [tex]\frac{\sqrt{5}\sqrt{2}}{2\sqrt{2}\sqrt{2}} \ \ or \ - \frac{\sqrt{5}\sqrt{2}}{2\sqrt{2}\sqrt{2}}[/tex]

final answer, simplified:

  • [tex]\rf x=\frac{\sqrt{10}}{4},\:x=-\frac{\sqrt{10}}{4}[/tex]
ᴜᴋɪʏᴏ

Answer:

[tex]x = \boxed{ \frac{\sqrt{10}}{4} , - \frac{\sqrt{10}}{4} }[/tex]

Step-by-step explanation:

We can solve this question by using the method of finding the square root.

The given equation is:

[tex]8x ^ { 2 } -3=2[/tex]

Add 3 to both the sides of the equation.

[tex]8x^{2}=2+3[/tex]

Now, add 2 & 3 to get 5.

[tex]8x^{2}=5[/tex]

Dividing both the sides of the equation by 8, we get...

[tex]x^{2}=\frac{5}{8}[/tex]

Now, take the square root of both the sides of the equation...

[tex]x =\sqrt{ \frac{ 5 }{ 8 } } \\x = \frac{\sqrt{5}}{\sqrt{8}} \\[/tex]

Rationalize the denominator.

[tex]x = \frac{\sqrt{5}}{2\sqrt{2}} \\x = \frac{\sqrt{5}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}} \\x = \frac{\sqrt{5}\sqrt{2}}{2\times 2} \\x = \frac{\sqrt{10}}{2\times 2} \\x = \boxed{ \frac{\sqrt{10}}{4} , - \frac{\sqrt{10}}{4} }[/tex]

[tex]\rule{200}{3}[/tex]

  • The value of x =  [tex]\boxed{ \frac{\sqrt{10}}{4} , - \frac{\sqrt{10}}{4} }[/tex]

[tex]\rule{200}{3}[/tex]

Hope this helps!

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